Global solvability to a two-dimensional chemotaxis-Euler system with Robin boundary conditions on oxygen

Abstract

This paper is concerned with the global solvability of a chemotaxis-Euler system in bounded domains of ${\mathbb{R}}^2$. Completing the system with physical boundary conditions, we firstly prove local well-posedness of the corresponding initial-boundary value problem and then present some blow-up criteria. We also show that the local solutions can be extended globally in time under suitable smallness assumptions on initial and boundary data.